In this paper, we present some efficient numerical algorithms for solving nonlinear
equations based on Newton–Raphson method by using modified homotopy perturbation
method. The modified Adomian decomposition method [S. Abbasbandy, Improving
Newton–Raphson method for nonlinear equations by modified Adomian
decomposition method, Appl. Math. Comput. 145 (2003) 887–893], is compared with
new algorithms. Some numerical illustrations are given to show the efficiency of
algorithms.
